Functional 3D components such as perfusion channels and mechanical actuation elements at cellular length scales can support cell survival and tissue maturation in tissue modeling devices. These advanced requirements call for increasingly complex materials and 3D fabrication methods. Here, a high‐resolution dual‐material 3D printing concept is developed, where distinct materials are produced locally by orthogonal chemical reactions depending on the illumination wavelength. A tough, stiff epoxy network results from cationic polymerization in UV light, while a soft and diffusion‐open hydrogel forms by free‐radical polymerization initiated by blue light. Thus, dual‐exposure allows for selection of material properties in every voxel, while retaining the 3D design flexibility associated with stereolithography. This enables single‐process fabrication of devices integrating mechanically stable chip‐to‐world interconnects and compliant, diffusion‐open perfusable channel components of 150 µm in width and height, while also allowing structural and mechanical feature dimensions down to 60 µm. A perfusion chip capable of creating a stable uniaxial chemical gradient by passive dye diffusion through hydrogel sections, and a negative Poisson ratio structure based on the interplay between stiff rotators and compliant hinges, are manufactured as proof‐of‐concept microdevices. Lastly, week‐long culture of hydrogel‐encapsulated human liver cells demonstrates the cytocompatibility of both materials.